where \(\tilde{p}=1-\frac{1}{\sqrt{M}}\)  and \(\tilde{a}=\sqrt{\frac{3}{M-1}}\) .
Similarly, for BPSK, i.e. when \(M_I = 2, M_Q = 1\)  and \(\beta = 0\) , one can obtain ASER expression of BPSK which is given in (REF ). It is important to mention that (REF ) and (REF ) are the closed-form solutions of [1]} and [1]}, respectively.
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